As mentioned in [1]}, the first numerical analysis of ROM closures was performed in [2]}, where error bounds for the time discretization of the Smagorinsky model (i.e., a ROM closure model developed on phenomenological arguments) were proven.
Error bounds for the time and space discretizations of the
Smagorinsky model were later proven in [3]} in an RBM context.
Error bounds for VMS closure models were proved in [4]}, [5]}, [6]}, [7]} (see also [8]}, [9]} for related work).
Finally, error bounds for the D2-VMS-ROM (REF ) were proved in [10]} (see also [11]} for related work).
